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arXiv · 2103.11748

Forcing the $\Pi^1_n$-Uniformization Property

Stefan Hoffelner
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Abstract

We generically construct a model in which the ${\Pi^1_3}$-uniformization property is true, thus lowering the best known consistency strength from the existence of $M_1^{\#}$ to just $\mathsf{ZFC}$. The forcing construction can be adapted to work over canonical inner models with Woodin cardinals, which yields, for the first time, universes where the $\Pi^1_{2n}$-uniformization property holds for $n >1$, thus producing models which contradict the natural $\mathsf{PD}$-induced pattern.

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Stefan Hoffelner. 2021-03-22. Forcing the $\Pi^1_n$-Uniformization Property. https://arxiv.org/abs/2103.11748

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